In photography, bokeh is basically a type of blur in the out-of-focus part of a photograph. Bokeh occurs because of the lens. One way to think about Bokeh is that it's "the way the lens renders out-of-focus points of light".
Some people have difference preferences for Bokeh. Some say there is bad bokeh and good bokeh but it's entirely subjective. Bokeh always occurs in parts of the scene that lie outside the depth of field. Photographers often intentionally use a shallow focus techniques to create images with prominent out-of-focus regions.
Bokeh is usually most visible around smaller background highlights however, bokeh is not limited to the highlights.
Here is a great example of the various different types of Bokeh you get for different prime lenses.
This video explains what it is quite well: